{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "sfh_all = pd.read_csv('data/sfhousing.csv', on_bad_lines='skip')\n",
    "\n",
    "\n",
    "def make_lamorinda(sfh):\n",
    "    return sfh.replace({\n",
    "        'city': {\n",
    "            'Lafayette': 'Lamorinda',\n",
    "            'Moraga': 'Lamorinda',\n",
    "            'Orinda': 'Lamorinda',\n",
    "        }\n",
    "    })\n",
    "\n",
    "four_cities = ['Berkeley', 'Lamorinda', 'Piedmont', 'Richmond']\n",
    "\n",
    "def parse_dates(sfh):\n",
    "    dates = pd.to_datetime(sfh['date'], format='%Y-%m-%d')\n",
    "    return sfh.assign(dates=dates).set_index('date')\n",
    "\n",
    "\n",
    "def subset(df):\n",
    "    return df.loc[(df['price'] < 4000000) &\n",
    "                  (df['bsqft'] < 12000) &\n",
    "                  (df['lsqft'] < 100000) &\n",
    "                  (df['city'].str.contains(\"Berkeley|Piedmont|Richmond|Lamorinda\")) &\n",
    "                  (df['dates'] > '2005-12-31') &\n",
    "                  (df['dates'] <= '2006-12-31')\n",
    "                 ]\n",
    "\n",
    "def log_vals(sfh):\n",
    "    return sfh.assign(log_price=np.log10(sfh['price']),\n",
    "                      log_bsqft=np.log10(sfh['bsqft']),\n",
    "                      log_lsqft=np.log10(sfh['lsqft']))\n",
    "\n",
    "def clip_br(sfh):\n",
    "    six_up = sfh.loc[sfh['br'] >=6, 'br'].unique()\n",
    "    new_bed = sfh['br'].replace(six_up, 6)\n",
    "    return sfh.assign(br=new_bed)\n",
    "\n",
    "def compute_ppsf(sfh):\n",
    "    return sfh.assign(\n",
    "    ppsf=sfh['price'] / sfh['bsqft'], \n",
    "    log_ppsf=lambda df: np.log10(df['ppsf']))\n",
    "\n",
    "\n",
    "sfh = (sfh_all\n",
    " .pipe(make_lamorinda)\n",
    " .pipe(parse_dates)\n",
    " .pipe(subset)\n",
    " .pipe(log_vals)\n",
    " .pipe(clip_br)\n",
    " .pipe(compute_ppsf) \n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "var_na = ['log_price', 'log_lsqft', 'log_bsqft', 'br']\n",
    "sfh = sfh.dropna(subset=var_na)\n",
    "sfh.drop([\"dates\",\"county\", \"zip\",\"street\",\"year\",\"datesold\"], axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Engineering for Categorical Measurements \n",
    "\n",
    "The first model we ever fit was the constant model in {numref}`Chapter %s <ch:modeling>`. There, we minimized squared loss to find the best-fitting constant:\n",
    "\n",
    "$$\n",
    "\\min_c \\sum_i (y_i - c)^2\n",
    "$$\n",
    "\n",
    "We can think of including a nominal feature in a model in a similar fashion. That is, we find the best-fitting constant to each subgroup of the data corresponding to a category: \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\min_{c_B} \\sum_{i \\in \\textrm{Berkeley}} (y_i - c_B)^2\n",
    "~~~&~~~  \\min_{c_L} \\sum_{i \\in \\textrm{Lamorinda}} (y_i - c_L)^2 \\\\\n",
    " \\min_{c_P} \\sum_{i \\in \\textrm{Piedmont}} (y_i - c_P)^2\n",
    "~~~&~~~ \\min_{c_R} \\sum_{i \\in \\textrm{Richmond}} (y_i - c_R)^2 \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Another way to describe this model is with *one-hot encoding*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One-hot encoding takes a categorical feature and creates multiple numeric\n",
    "features that have only the values 0 or 1.\n",
    "To one-hot encode a feature, we create new features, one for each unique category.\n",
    "In this case, since we have four cities—Berkeley, Lamorinda, Piedmont, and Richmond—we create four new features in a design matrix, called $X_{city}$.\n",
    "Each row in $X_{city}$ contains one value of 1 and it appears  in the column that corresponds to the city. All other columns contain 0 for that row.\n",
    "{numref}`Figure %s <fig:one-hot2>` illustrates this notion. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} figures/one-hot.svg\n",
    "---\n",
    "name: fig:one-hot2\n",
    "width: 100%\n",
    "---\n",
    "\n",
    "One-hot encoding for a categorical feature with six rows (left) and its resulting design matrix (right)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can concisely represent the model as follows:\n",
    "\n",
    "$$\n",
    "\\theta_B x_{i,B} ~+~ \\theta_L x_{i,L} ~+~ \\theta_P x_{i,P} ~+~ \\theta_R x_{i,R}\n",
    "$$\n",
    "\n",
    "Here, we have indexed the columns of the design matrix by $B$, $L$, $P$, and $R$, rather than $j$, to make it clear that each column represents a column of 0s and 1s where, say, a 1 appears for $x_{i,P}$ if the $i$th house is located in Piedmont. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "One-hot encoding creates features that have only 0-1 values. These features are also known as *dummy variable* or *indicator variable*.\n",
    "The term \"dummy variable\" is more common in econometrics, and the usage of \"indicator variable\" is more common in statistics.  \n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our goal is to minimize least square loss over $\\boldsymbol{\\theta}$:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\| \\mathbf{y} - \\textbf{X}\\boldsymbol{\\theta} \\|^2 &=\n",
    "\\sum_i (y_i - \\theta_B x_{i,B} ~+~ \\theta_L x_{i,L}  ~+~ \\theta_P x_{i,P} ~+~ \\theta_R x_{i,R})^2 \\\\\n",
    "& = \\sum_{i \\in Berkeley} (y_i - \\theta_B x_{i,B})^2 ~+~ \\sum_{i \\in Lamorinda} (y_i -\\theta_L x_{i,L})^2 \\\\\n",
    "~~~~~~~~& ~+~ \\sum_{i \\in Piedmont} (y_i -\\theta_P x_{i,P})^2 ~+~ \\sum_{i \\in Richmond} (y_i -\\theta_R x_{i,R})^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $\\boldsymbol{\\theta}$ is the column vector $[\\theta_B, \\theta_L, \\theta_P, \\theta_R]$. Notice that this minimization reduces to four minimizations, one for each city. That's the idea that we started with at the beginning of this section. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `OneHotEncoder` to create this design matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Berkeley</th>\n",
       "      <th>Lamorinda</th>\n",
       "      <th>Piedmont</th>\n",
       "      <th>Richmond</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2664</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2665</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>2666</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2667 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Berkeley  Lamorinda  Piedmont  Richmond\n",
       "0          1.0        0.0       0.0       0.0\n",
       "1          1.0        0.0       0.0       0.0\n",
       "2          1.0        0.0       0.0       0.0\n",
       "...        ...        ...       ...       ...\n",
       "2664       0.0        0.0       0.0       1.0\n",
       "2665       0.0        0.0       0.0       1.0\n",
       "2666       0.0        0.0       0.0       1.0\n",
       "\n",
       "[2667 rows x 4 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder\n",
    "\n",
    "enc = OneHotEncoder(\n",
    "    # categories argument sets column order\n",
    "    categories=[[\"Berkeley\", \"Lamorinda\", \"Piedmont\", \"Richmond\"]],\n",
    "    sparse=False,\n",
    ")\n",
    "\n",
    "X_city = enc.fit_transform(sfh[['city']])\n",
    "\n",
    "categories_city=[\"Berkeley\",\"Lamorinda\", \"Piedmont\", \"Richmond\"]\n",
    "X_city_df = pd.DataFrame(X_city, columns=categories_city)\n",
    "\n",
    "X_city_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit a model using these one-hot encoded features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_log = sfh['log_price']\n",
    "\n",
    "model_city = LinearRegression(fit_intercept=False).fit(X_city_df, y_log)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And examine the multiple $R^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-square for city model: 0.57\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(f\"R-square for city model: {model_city.score(X_city_df, y_log):.2f}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we only know the city where a house is located, the model does a reasonably good job of estimating its sale price. Here are the coefficients from the fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.87, 6.03, 6.1 , 5.67])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_city.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected from the box plots, the estimated sale price (in log $) depends on the city. But if we know the size of the house as well as the city, we should have an even better model. We saw earlier that the simple log–log model that explains sale price by house size fits reasonably well, so we expect that the city feature (as one-hot encoded variables) should further improve the model. \n",
    "\n",
    "Such a model looks like this:\n",
    "\n",
    "$$\n",
    "y_i ~\\approx~ \\theta_1x_i +  \\theta_B x_{i,B} ~+~ \\theta_L x_{i,L} \n",
    "~+~ \\theta_P x_{i,P} ~+~ \\theta_R x_{i,R}\n",
    "$$\n",
    "\n",
    "Notice that this model describes the relationship between log(price), which is represented as $y$, and log(size), which is represented as $x$, as linear with the same coefficient for log(size) for each city.\n",
    "But the intercept term depends on the city:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "y_i ~&\\approx~ \\theta_1x_i +  \\theta_B  ~~&\\text{for houses in Berkeley} \\\\\n",
    "y_i ~&\\approx~ \\theta_1x_i + \\theta_L  ~~&\\text{for houses in Lamorinda}\\\\\n",
    "y_i ~&\\approx~ \\theta_1x_i + \\theta_P  ~~&\\text{for houses in Piedmont}\\\\\n",
    "y_i ~&\\approx~ \\theta_1x_i + \\theta_R  ~~&\\text{for houses in Richmond}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We next make a facet of scatterplots, one for each city, to see if this relationship roughly holds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hovertemplate": "city=Berkeley<br>Building size (log ft^2)=%{x}<br>Sale price (log USD)=%{y}<extra></extra>",
         "legendgroup": "",
         "marker": {
          "color": "#1F77B4",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter(sfh, x='log_bsqft', y='log_price', \n",
    "                 facet_col='city', facet_col_wrap=2,\n",
    "                 labels={'log_bsqft':'Building size (log ft^2)',\n",
    "                        'log_price':'Sale price (log USD)'},\n",
    "                 width=500, height=400)\n",
    "\n",
    "fig.update_layout(margin=dict(t=30))\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shift is evident in the scatter plot. We concatenate our two design matrices together to fit the model that includes size and city: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>log_bsqft</th>\n",
       "      <th>Berkeley</th>\n",
       "      <th>Lamorinda</th>\n",
       "      <th>Piedmont</th>\n",
       "      <th>Richmond</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.14</td>\n",
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       "    <tr>\n",
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       "      <td>3.31</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.96</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>2664</th>\n",
       "      <td>3.16</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>2665</th>\n",
       "      <td>3.47</td>\n",
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       "    <tr>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>2666 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      log_bsqft  Berkeley  Lamorinda  Piedmont  Richmond\n",
       "1          3.14       1.0        0.0       0.0       0.0\n",
       "2          3.31       1.0        0.0       0.0       0.0\n",
       "3          2.96       1.0        0.0       0.0       0.0\n",
       "...         ...       ...        ...       ...       ...\n",
       "2664       3.16       0.0        0.0       0.0       1.0\n",
       "2665       3.47       0.0        0.0       0.0       1.0\n",
       "2666       3.44       0.0        0.0       0.0       1.0\n",
       "\n",
       "[2666 rows x 5 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_size = sfh['log_bsqft'] \n",
    "\n",
    "X_city_size = pd.concat([X_size.reset_index(drop=True), X_city_df], axis=1)\n",
    "X_city_size.drop(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's fit a model that incorporates the quantitative feature, the house size, and the qualitative feature, location (city):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_city_size = LinearRegression(fit_intercept=False).fit(X_city_size, y_log)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intercepts reflect which cities have more expensive houses, even taking into account the size of the house:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62, 3.89, 3.98, 4.03, 3.75])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_city_size.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-square for city and log(size):  0.79\n"
     ]
    }
   ],
   "source": [
    "print(f\"R-square for city and log(size):\",\n",
    "      f\" {model_city_size.score(X_city_size, y_log):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This fit, which includes the nominal variable `city` and the log-transformed house size, is better than both the simple log–log model with house size and the model that fits constants for each city."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we dropped the intercept from the model so that each subgroup has its own intercept. \n",
    "However, a common practice is to remove one of the one-hot encoded features from the design matrix and keep the intercept. For example, if we drop the feature for Berkeley houses and add the intercept, then the model is:\n",
    "\n",
    "$$\n",
    "\\theta_0 ~+~ \\theta_1x_i ~+~ \\theta_L x_{i,L} ~+~ \\theta_P x_{i,P} ~+~ \\theta_R x_{i,R}\n",
    "$$\n",
    "\n",
    "The meaning of the coefficients for the dummy variables has changed in this representation.\n",
    "For example, consider this equation for a house in Berkeley and a house in Piedmont:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\theta_0 & ~+~ \\theta_1x_i ~~&\\text{for a house in Berkeley} \\\\\n",
    "\\theta_0 & ~+~ \\theta_1x_i + \\theta_P  ~~&\\text{for a house in Piedmont}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In this representation, the intercept $\\theta_0$ is for Berkeley houses, and the coefficient $\\theta_P$ measures the typical difference between a Piedmont house and a Berkeley house. In this representation, we can more easily compare \n",
    "$\\theta_P$ to 0 to see if these two cities have essentially the same average price. \n",
    "\n",
    "If we include the intercept and all of the city variables, then \n",
    "the columns of the design matrix are linearly dependent, which means that we can't solve for the coefficients. Our predictions will be the same in either case, but there will not be a unique solution to the minimization.\n",
    "\n",
    "We also prefer the representation of the model that drops one dummy variable and includes an intercept term when we  include one-hot encodings of two categorical variables. This practice maintains consistency in the interpretation of the coefficients.     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We demonstrate how to build a model with two sets of dummy variables, using the `statsmodels` library. This library uses a formula language to describe the model to fit, so we don't need to create the design matrix ourselves. We import the formula API, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first repeat our fit of the model with the nominal variable `city` and house size to show how to use the formula language and compare the results: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_size_city = smf.ols(formula='log_price ~ log_bsqft + city',\n",
    "                          data=sfh).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The string provided for the `formula` parameter describes the model to fit. The model has `log_price` as the outcome and fits a linear combination of `log_bsqft` and `city` as explanatory variables. Notice that we do not need to create dummy variables to fit the model. Conveniently, `smf.ols` does the one-hot encoding of the city feature for us. The fitted coefficients of the following model, include an intercept term and drop the Berkeley indicator variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept            3.89\n",
      "city[T.Lamorinda]    0.09\n",
      "city[T.Piedmont]     0.14\n",
      "city[T.Richmond]    -0.15\n",
      "log_bsqft            0.62\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(model_size_city.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to drop the intercept, we can add –1 to the formula, which is a convention that indicates dropping the column of ones from the design matrix. In this particular example, the space spanned by all of the one-hot encoded features is equivalent to the space spanned by the 1 vector and all but one of the dummy variables, so the fit is the same. However, the coefficients are different as they reflect the different parameterization of the design matrix: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "city[Berkeley]     3.89\n",
       "city[Lamorinda]    3.98\n",
       "city[Piedmont]     4.03\n",
       "city[Richmond]     3.75\n",
       "log_bsqft          0.62\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "smf.ols(formula='log_price ~ log_bsqft + city - 1', data=sfh).fit().params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, we can add interaction terms between the city and size variables to allow each city to have a different coefficient for size. We specify this in the formula by adding the term `log_bsqft:city`. We don't go into details here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's fit a model with two categorical variables: the number of bedrooms and the city. Recall that we earlier reassigned the count of bedrooms that were above 6 to 6, which essentially collapses 6, 7, 8, ... into the category, 6+. We can see this relationship in the box plots of price (log \\$) by the number of bedrooms: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.box(sfh, x=\"br\", y=\"log_price\", width=450, height=250,\n",
    "      labels={'br':'Number of bedrooms','log_price':'Sale price (log USD)'})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relationship does not appear linear: for each additional bedroom, the sale price does not increase by the same amount. Given that the number of bedrooms is discrete, we can treat this feature as categorical, which allows each bedroom encoding to contribute a different amount to the cost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_size_city_br = smf.ols(formula='log_price ~ log_bsqft + city + C(br)',\n",
    "                             data=sfh).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have used the term `C(br)` in the formula to indicate that we want the number of bedrooms, which is numeric, to be treated like a categorical variable. \n",
    "\n",
    "Let’s examine the multiple $R^2$ from the fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_size_city_br.rsquared.round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The multiple $R^2$ has not increased even though we have added five more one-hot encoded features. The $R^2$ is adjusted for the number of parameters in the model and by this measure\n",
    "is no better than the earlier one that included only city and size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we introduced feature engineering for qualitative features. We saw how the one-hot encoding technique lets us include categorical data in linear models and gives a natural interpretation for model parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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